Photon energy calculator

Wavelength (λ) Option A

— OR —

Frequency (f) Option B

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Photon Energy (E)

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Joules: ---

How it works?

This calculator computes single photon energy based on the Planck-Einstein relation. Since frequency and wavelength are inversely proportional, the energy is derived using physical constants:

$$ E = h \cdot f $$ Using Frequency

$$ E = \frac{h \cdot c}{\lambda} $$ Using Wavelength

Constants:

h : Planck's Constant ($ \approx 6.626 \times 10^{-34} \, \text{J}\cdot\text{s} $)
c : Speed of Light ($ \approx 3.00 \times 10^8 \, \text{m/s} $)
E : Photon Energy (Joules)

The Electron-Volt (eV) Conversion

Photonics often uses Electron-Volts (eV) instead of Joules. The calculator converts this using the elementary charge:

$$ E_{\text{(eV)}} = \frac{E_{\text{(Joules)}}}{1.602 \times 10^{-19}} $$

How does the Photon Energy Calculator work?

In classical physics, light is treated as a continuous wave. However, in the realm of quantum mechanics, light behaves as individual "packets" of quantized energy known as photons. The energy contained within a single photon is directly proportional to its electromagnetic frequency and inversely proportional to its wavelength.

This photon energy calculator bridges the gap between these two worlds. It allows engineers and physicists to instantly convert between the color of light (wavelength in nm or frequency in Hz) and its energy potential (Joules or Electron-Volts).

The Photon Energy Formula

The calculation is based on the fundamental Planck-Einstein relation. This law states that the energy (E) of a photon is equal to its frequency (f) multiplied by Planck's constant (h).

E = h × f OR E = (h × c) / λ

Where:
• E = Photon Energy (Joules)
• h = Planck’s Constant (6.626 × 10⁻³⁴ J·s)
• c = Speed of Light (approx. 3 × 10⁸ m/s)
• λ (Lambda) = Wavelength of the light (meters)

Units: Joules vs. Electron-Volts (eV)

While the standard unit for energy is the Joule (J), it is inconveniently large for quantum calculations (resulting in tiny numbers like 10⁻¹⁹). Therefore, photonics engineers prefer the Electron-Volt (eV).

1 eV is defined as the energy gained by an electron accelerating through a potential difference of 1 volt. A handy rule of thumb for this calculator is the relationship: Energy (eV) ≈ 1240 / Wavelength (nm).

Key Applications for Photon Energy

1. Semiconductor Bandgap Engineering

For a Light Emitting Diode (LED) or Laser Diode to function, an electron must drop across a specific "Bandgap." This drop releases a photon. Engineers use a photon energy calculator to match the material's bandgap (in eV) to the desired output color (in nm). For example, a 1.1 eV bandgap produces infrared light, while a 3.0 eV gap creates blue/UV light.

2. Photovoltaics & Solar Efficiency

Solar panels rely on the Photoelectric Effect. A solar cell can only convert photons that carry enough energy to knock an electron loose from the silicon lattice. Photons with energy lower than the bandgap pass through generating heat, not power. Calculating this threshold is critical for efficiency optimization.

3. Photochemistry & Curing

Chemical reactions, such as UV curing of resins or biological imaging, require a minimum "Activation Energy" to proceed. By converting the activation energy into wavelength, chemists can determine exactly which UV source (e.g., 365 nm vs 405 nm) will trigger the reaction without damaging the sample.

4. X-Ray & High Energy Physics

As the electromagnetic spectrum moves into X-rays and Gamma rays, describing light by wavelength becomes cumbersome (e.g., 0.00001 nm). In these high-energy fields, scientists abandon wavelength entirely and use this calculator to describe photons purely by their energy in kiloelectron-volts (keV) or MeV.

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